Q. 14 Given points A, B, and C. Find A... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 13: Q. 14 (page 526)

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?
If so, which point lies between the other two?
14. A(5, -5), B(0, 5), C(2, 1)

Short Answer

Expert verified

The values of $A B = 5 \sqrt{5}, B C = 2 \sqrt{5}, A C = 3 \sqrt{5}$ .

A, B, Care collinear.

PointC lies between the other two points.

Step by step solution

Step-1 – Given

The given points are $A (5, 鈭� 5), B (0, 5), C (2, 1)$ .

Step-2 – To determine

We have to find the lengths AB, BCand AC.Then have to check ifA, B, C are collinear. And determine that which point lies between the other two.

Step-3 – Calculation

Using the distance formula, the distance between A and B is:

$\begin{array}{l} A B = \sqrt{{(0 鈭� 5)}^{2} + {(5 鈭� (鈭� 5))}^{2}} \\ A B = \sqrt{{(0 鈭� 5)}^{2} + {(5 + 5)}^{2}} \\ A B = \sqrt{{(鈭� 5)}^{2} + {(10)}^{2}} \\ A B = \sqrt{25 + 100} \\ A B = \sqrt{125} \\ A B = 5 \sqrt{5} \end{array}$

Using the distance formula, the distance between B and C is:

$\begin{array}{l} B C = \sqrt{{(2 鈭� 0)}^{2} + {(1 鈭� 5)}^{2}} \\ B C = \sqrt{{(2)}^{2} + {(鈭� 4)}^{2}} \\ B C = \sqrt{4 + 16} \\ B C = \sqrt{20} \\ B C = 2 \sqrt{5} \end{array}$

Using the distance formula, the distance between A and C is:

$\begin{array}{l} A C = \sqrt{{(2 鈭� 5)}^{2} + {(1 鈭� (鈭� 5))}^{2}} \\ A C = \sqrt{{(2 鈭� 5)}^{2} + {(1 + 5)}^{2}} \\ A C = \sqrt{{(鈭� 3)}^{2} + {(6)}^{2}} \\ A C = \sqrt{9 + 36} \\ A C = \sqrt{45} \\ A C = 3 \sqrt{5} \end{array}$

Hence,

$\begin{array}{l} B C + A C = A B \\ A B = 2 \sqrt{5} + 3 \sqrt{5} \\ A B = 5 \sqrt{5} \end{array}$

So, the values of $A B = 5 \sqrt{5}, B C = 2 \sqrt{5}, A C = 3 \sqrt{5}$ .

A, B, Care collinear.

PointC lies between the other two points.

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91影视

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?
If so, which point lies between the other two?
14. A(5, -5), B(0, 5), C(2, 1)

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

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91影视

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?If so, which point lies between the other two?14. A(5, -5), B(0, 5), C(2, 1)

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?
If so, which point lies between the other two?
14. A(5, -5), B(0, 5), C(2, 1)